Characteristics of randomly connected threshold-element networks and network systems

The characteristics of the networks which are composed of many randomly connected threshold elements are investigated with the intention of understanding some aspects of information processing in nervous systems. In these networks, the statistical properties of connection are sufficient to determine the characteristics. Information is carried by the activity level of a network which designates the rate of exciting elements. Dynamics of the activity level is studied. Two statistical parameters, which are sufficient to determine the characteristics of networks, are extracted and the networks are categorized into three classes by these parameters. One is monostable, having only one stable activity level. Another is monostable or bistable according to the average threshold value of the elements. The third is astable or monostable. The characteristics of these three kinds of networks are analyzed in detail. Various systems can be obtained by connecting random networks, where the average thresholds of component networks can be controlled by other networks. The system performances are given. A stable oscillation of a long period is shown to exist in a system composed of two kinds of elements, i.e., excitatory and inhibitory elements, by randomly connecting them. A model for association of ideas is presented.